Gaussian Random Processes

I A Ibragimov

ISBN 10: 038790302X / ISBN 13: 9780387903026

Published by Springer New York Dez 1978, 1978

About this Item

Neuware - The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a 'random process segment' and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known 'strong mixing condition') as well as to describe the subclasses associated with 'mixing rate'. The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of 'distinguishing a signal from stationary noise'. Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.

Seller Inventory # 9780387903026

Bibliographic Details

• Title: Gaussian Random Processes
• Publisher: Springer New York Dez 1978
• Publication Date: 1978
• Language: English
• ISBN 10: 038790302X
• ISBN 13: 9780387903026
• Binding: Buch
• Condition: Neu
• Dimensions: 234W x 156H x 18D millimeters 234 millimeters width by 156 millimeters height by 18 millimeters depth
• Weight: 585 grams

About this title

Synopsis

The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva­ lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par­ ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam­ ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys­ tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.

Language Notes

Text: English, Russian (translation)